A064556 Ramanujan's tau function (or tau numbers (A000594)) for 10^n.

1, -115920, 37534859200, -30328412970240000, -482606811957501440000, -2983637890141033828147200000

Offset: 0

Author

Robert G. Wilson v, Jan 04 2003

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..181
• Index entries for linear recurrences with constant coefficients, signature (-115920, 124097412800, -11592000000000000, -10000000000000000000000).

Crossrefs

Cf. A000594, A035174.

Programs

Mathematica

Table[ RamanujanTau[10^n], {n, 0, 5}]

PARI

taup(p, e)={
    if(e==1,
        (65*sigma(p, 11)+691*sigma(p, 5)-691*252*sum(k=1, p-1, sigma(k, 5)*sigma(p-k, 5)))/756
    ,
        my(t=taup(p, 1));
        sum(j=0, e\2,
            (-1)^j*binomial(e-j, e-2*j)*p^(11*j)*t^(e-2*j)
        )
    )
};
a(n)=taup(5,n)*taup(2,n) \\ Charles R Greathouse IV, Sep 06 2015

Perl

use bigint; use ntheory ":all"; say "$ ",ramanujan_tau(10 ** $) for 0..19; # Dana Jacobsen, Sep 05 2015